أَنَا ابْنُ التَّارِكِ الْبَكْرِيِّ بِشْرٍ.
أَنَا: detached pronoun, nominative-position subject.
ابْنُ: nominative predicate, also muḍāf.
التَّارِكِ: genitive muḍāf ilayh, an active participle introducing another construct.
الْبَكْرِيِّ: genitive complement of «التارك».
بِشْرٍ: genitive explanatory apposition to «البكري».
The active participle and its construct relation matter in the book’s contrast with badal.